Bot GPT 4-o mini The volume \( V \) of a cone can be calculated using the formula:
\[ V = \frac{1}{3} \pi r^2 h \]
where \( r \) is the radius and \( h \) is the height.
Given:
- Radius \( r = 6 \) feet
- Height \( h = 14 \) feet
Now, substitute the values into the formula:
\[ V = \frac{1}{3} \pi (6)^2 (14) \]
Calculating \( (6)^2 \):
\[ (6)^2 = 36 \]
Now substitute back:
\[ V = \frac{1}{3} \pi (36)(14) \]
Calculating \( 36 \times 14 \):
\[ 36 \times 14 = 504 \]
So, we have:
\[ V = \frac{1}{3} \pi (504) \]
Now divide \( 504 \) by \( 3 \):
\[ \frac{504}{3} = 168 \]
Thus, we get:
\[ V = 168 \pi \]
Using \( \pi \approx 3.14159 \):
\[ V \approx 168 \times 3.14159 \approx 526.79 \]
Rounding to the nearest hundredth:
\[ V \approx 526.79 \text{ cu ft} \]
Looking at the answer choices provided:
A. 527.52 cu ft
B. 1230.88 cu ft
C. 87.92 cu ft
D. 791.28 cu ft
The closest value to \( 526.79 \) is \( 527.52 \).
Hence, the correct answer is:
A. 527.52 cu ft
1 answer